Phase Extraction In Optical Processing

ABSTRACT

A method of optical data processing, comprising: providing a first data set to be optically transformed using a transform; combining a reference data set with said first data set to generate coherent light, encoding a combined data set; optically and coherently transforming said light that encodes the combined data set, into coherent light that encodes a transformed combined data set; obtaining a transformed reference data set by determining the effect said optical transform has on light encoding said reference data set; and extracting a second data set that represents a transform of said first data set, from an intensity portion of light encoding said transformed combined data set, using said transformed reference data set to extract a phase of at least one element of said second data set.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.09/979,182 filed Feb. 25, 2002, which is a U.S. national filing of PCTApplication No. PCT/IL00/00284, filed May 19, 2000. This application isalso a continuation in part of PCT application No. PCT/IL99/00479, filedSep. 5, 1999, now U.S. application Ser. No. 09/926,547, filed on Mar. 5,2002, the disclosures of which are incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to optical methods and apparatus for performingcomputations and in particular to transforming a first data set into asecond data set by a linear transformation and determining the phase ofdata elements in the second data set.

BACKGROUND OF THE INVENTION

Optical data processing can often be used to process data more rapidlyand efficiently than conventional computational methods. In particular,optical methods can be used to perform linear transformations of datasets rapidly and efficiently.

For example, it is well known that converging lenses can be used tosubstantially “instantaneously” transform a first image into a secondimage that is a Fourier transform of the first image. It is to be notedthat the Fourier transform is a relationship between the complexamplitudes of light in the images and not between the intensities oflight in the images. The same is generally true with respect to othertransformations of images, the transformation is a transformation ofcomplex amplitudes of light and not intensities of light. It istherefore to be understood that when a second image is said to be aFourier, or other, transform of a first image, what is meant is that thespatial pattern of the complex amplitude of light in the second image isthe Fourier, or other, transform of the spatial pattern of the complexamplitude of light in the first image.

If the first image is coded with data, the second image is coded withdata that is the Fourier transform of the data in the first image. Asuitable optical processor can therefore provide substantial advantagesin comparison to a conventional data processor when a spectral analysisof a data set is desired. However, a Fourier transform of a data set ingeneral involves complex numbers, even if the data set comprises onlyreal numbers. Therefore, in order to properly detect an “optical”Fourier transform of a data set, phase as well as intensity of light ofan image representing the Fourier transform must be detected. While thiscan be accomplished, most light detectors are generally sensitive onlyto light intensity and are not responsive to phase.

It is therefore generally more convenient to determine values for datarepresented by an image from only the intensity of light in the image.Consequently, it is usually advantageous to process data optically usingmethods that generate only real numbers from the data.

For example, it is often preferable to optically process data coded inan image in accordance with a cosine transform to perform a spectralanalysis of the data rather than a Fourier transform. The cosinetransform of a real data set generates real values. However, whereas acosine transform of a real data set does not generate complex numbers itdoes, usually, generate both positive and negative numbers. Therefore,while most of the information in an optical cosine transform of an imagecan be acquired from measurements of intensity of light in the image,sign information is not preserved in the intensity measurements. As aresult, an optical processor that transforms an input image into anoutput image that represents the cosine transform of the input imagerequires a means for determining which of the numbers represented by theoutput image are positive and which are negative.

K. W. Wong et al, in an article entitled “Optical cosine transform usingmicrolens array and phase-conjugate mirror ”, Jpn J. Appl. Phys. vol.31, 1672-1676, the disclosure of which is incorporated herein byreference, describes a method of distinguishing positive and negativedata in a cosine transform of an image.

The problem of distinguishing the sign of numbers represented by animage when only the intensity of light in the image is measured is ofcourse not limited to the case of data optically generated by a cosinetransform. The problem affects all real linear transforms, such as forexample the sine and discrete sine transforms and the Hartley transform,when the transforms are executed optically and only their intensitiesare sensed, if they generate both positive and negative values from areal data set.

SUMMARY OF THE INVENTION

An aspect of some embodiments of the present invention relates toproviding a method for determining the sign of data encoded in an outputimage of a linear optical processor using measurements of intensity oflight in the output image, hereinafter referred to as a “data outputimage”. The data output image is assumed to be generated by theprocessor responsive to an input image, a “data input image”, encodedwith input data that is real. The input data is either all positive orall negative. For clarity of presentation it is assumed that the inputdata is all positive.

According to an aspect of some embodiments of the present invention, areference input image is defined for the optical processor. Magnitudeand phase of amplitude of a “reference” output image generated by theprocessor responsive to the input reference image are used to determinethe sign of data represented by the data output image.

The operation of a linear optical processor may be described by theequation F(u,v)=O(u,v:x,y)f(x,y). In the equation f(x,y) is a complexamplitude of light in an input image, i.e. a data input image, thatrepresents input data, which data input image is located on an inputplane of the processor, and x and y are coordinates of the input plane.Similarly, F(u,v) is a complex amplitude of light in a data output imagethat the processor generates responsive to f(x,y). The data output imageis located on an output plane of the processor having positioncoordinates u and v corresponding respectively to position coordinates xand y of the input plane. Intensity of light in the data input image isequal to |f(x,y)|² and intensity of light in the data output image isequal to |F(u,v)|².

O(u,v:x,y) represents any continuous or discrete linear operator thattransforms a first real data set into a second real data set. O(u,v:x,y)may for example represent the continuous or discrete sine or cosinetransform or the Hartley transform. For continuous lineartransformations u, v, x and y are continuous and multiplication in theequation representing operation of the processor represents integrationover the x, y coordinates. For discrete linear operators u, v, x, and yare discrete coordinates and multiplication represents summation overthe x, y coordinates.

Since, in accordance with embodiments of the present invention, theinput data is assumed to be real and positive, the phase of f(x,y) isconstant and input data is represented by the magnitude of f(x,y).F(u,v) also represents a real data set. However F(u,v) may have bothpositive and negative data. Data having positive values are representedby values of F(u,v) having a same first phase. Data having negativevalues are represented by values of F(u,v) having a same second phase180° different from the first phase.

Let the reference input image and its corresponding reference outputimage be represented by r(x,y) and R(u,v). Both r(x,y) R(u,v), andintensity of light in the reference output image |R(u,v)|² are known. Itis to be noted that it is possible to define and synthesize anypredefined reference function r(x,y) and use it for sign reconstructionin accordance with embodiments of the present invention. Whereasdescriptions of the present invention assume that r(x,y) is real theinvention is not limited to the reference image being real. Magnitudeand phase of R(u,v) are known from the transform that the opticalprocessor executes and can be checked experimentally using methods knownin the art. Preferably, r(x,y) is real. Therefore R(u,v) preferablycorresponds to a real data set. In some embodiments of the presentinvention R(u,v) is a real data set comprising values all of which havea same sign. In some embodiments of the present invention the data setcomprises one of or a combination of positive, negative and complexvalues.

In accordance with an embodiment of the present invention, to determineboth the magnitude and sign of F(u,v) the intensity of the data outputimage |F(u,v|² is measured. In addition, in accordance with anembodiment of the present invention, a combined input imagec(x,y)=f(x,y)+r(x,y) are processed by the processor to provide acombined output image C(u,v)=F(u,v)+R(u,v). Intensity of light in thecombined output image, which is equal to|C(u,v)|²=|F(u,v)|²+|R(u,v)|²+2F(u,v)R(u,v), is measured. Since|F(u,v)|², |R(u,v)|² and R(u,v) are known, the sign of F(u,v) can bedetermined from the “interference” term 2F(u,v)R(u,v).

It is to be noted that not only sign of F(u,v) can be determined from|C(u,v)|², |F(u,v)|², |R(u,v)|² and R(u,v). In general,(|C(u,v)|²−|F(u,v)|²−|R(u,v)|²)/2R(u,v) provides a magnitude and a phasefor F(u,v). In some cases the phase is known to within an ambiguity, forexample, a symmetry ambiguity or a 180°. In some embodiments of theinvention the ambiguity is removed and the phase extracted bydetermining a combined image C(u,v) for two or more different referenceimages r(x,y). The phase can be extracted for example by solving forF(u,v) using the two combined and reference images.

In some embodiments of the present invention the reference image ischosen so that |R(u,v)|≧|F(u,v)| for all values of u and v for whichR(u,v) and F(u,v) have opposite signs. For these embodiments of thepresent invention only the combined input image c(x,y)=f(x,y)+r(x,y) isprocessed by the processor to determine both the magnitude and sign ofF(u,v). If the intensity of light in the combined image minus theintensity light in the reference image at a point (u,v) in the outputplane of the processor is greater than zero, the signs F(u,v) and R(u,v)are the same at the point. If on the other hand the difference is lessthan zero, the signs of F(u,v) and R(u,v) are opposite. Since the signof R(u,v) is known, the sign of F(u,v) is known. The magnitude of F(u,v)at the point can be determined from the intensity |C(u,v)|² and theknown magnitude and sign of R(u,v) by solving a quadratic equation.

An aspect of some embodiments of the present invention relates toproviding an improved method for generating a cosine transform of an“input” image using an optical processor that generates a Fouriertransformed output image from an input image.

In accordance with an embodiment of the present invention, a firstFourier image that is a Fourier transform of the input image isgenerated by the optical processor and the intensity of the Fourierimage measured and stored. A second Fourier image is generated by theoptical processor from the input image plus a known first referenceimage and the intensity of the second Fourier image is measured andstored. The input image is parity transformed to generate a second inputimage, referred to as a “parity image”. A third Fourier image, which isa Fourier transform of the parity image is generated and its intensitymeasured and stored. A fourth Fourier image is generated which is aFourier transform of the parity image plus a known second referenceimage. The intensities of the four Fourier images and the amplitudes ofthe known reference images are used to determine the cosine transform ofthe input image. In some embodiments of the present invention the firstand second reference images are the same.

There is thus provided in accordance with an exemplary embodiment of theinvention, a method of optical data processing, comprising:

-   -   providing a first data set to be optically transformed using a        transform;    -   combining a reference data set with said first data set to        generate a combined data set;    -   optically transforming said combined data set into a transformed        combined data set; and    -   extracting a second data set that represents a transform of said        first data set, from an amplitude portion of said transformed        combined data set, using said reference image to extract a phase        of at least one element of said second data set. Optionally,        said transformed combined data set is detected using a power        detector. Alternatively or additionally, said transformed        combined data set is encoded using incoherent light.

In an exemplary embodiment of the invention, said transformed combineddata set is a discrete data set. Alternatively or additionally, saidfirst data set comprises a one-dimensional data set. Alternatively, saidfirst data set comprises a two-dimensional data set. Optionally, saidfirst data set comprises an image.

In an exemplary embodiment of the invention, said first data setcomprises at least one positive value. Alternatively or additionally,said first data set comprises at least one negative value. Alternativelyor additionally, said first data set comprises at least one complexvalue.

In an exemplary embodiment of the invention, extracting comprisesextracting using electronic processing.

In an exemplary embodiment of the invention, combining a reference dataset comprises adding at least one additional value to an existingelement of said first data set. Alternatively or additionally, combininga reference data set comprises replacing at least one existing elementof said first data set with an element from a second data set.Optionally, the method comprises compensating for an effect of saidreplaced value after said extraction. Optionally, said compensatingcomprises compensating using electronic processing.

In an exemplary embodiment of the invention, combining a reference dataset comprises adding at least one additional value alongside existingelements of said first data set. Optionally, said at least oneadditional value is arranged at a corner of a matrix layout of saidfirst data set.

In an exemplary embodiment of the invention, the method comprisesselecting said reference image to create a desired offset in saidtransformed combined data set. Optionally, said selecting takes intoaccount system imperfections. Alternatively or additionally, said offsetis substantially uniform. Alternatively, said offset is substantiallynon-uniform.

In an exemplary embodiment of the invention, said reference data is atleast one delta-function. Optionally, said reference data comprises aplurality of delta-functions. Alternatively or additionally, said atleast one delta function has an amplitude substantially greater thanthat of any of the data elements of said first data set.

In an exemplary embodiment of the invention, said at least one deltafunction has an amplitude substantially greater than that of any of thedata elements of said first data set that have a certain phase.

In an exemplary embodiment of the invention, said at least one deltafunction has an amplitude substantially greater than an amplitude of acomponent of any of the data elements of said first data set that fit ina certain phase range.

In an exemplary embodiment of the invention, said at least one deltafunction has an amplitude not greater than that of any of the dataelements of said first data set.

Optionally, said amplitudes are measured as amplitudes of transformelements.

In an exemplary embodiment of the invention, combining comprisescombining electronically and generating a combined modulated light beam.

Alternatively, combining comprises combining optically. Optionally,combining comprises creating said reference image optically. Optionally,said reference image is created using a refractive optical element.Alternatively, said reference image is created using a dedicated lightsource.

In an exemplary embodiment of the invention, said transform is aFourier-derived transform.

In an exemplary embodiment of the invention, said transform is a DCTtransform.

In an exemplary embodiment of the invention, extracting a phasecomprises extracting only a sign.

BRIEF DESCRIPTION OF FIGURES

A description of exemplary embodiments of the present invention follows.In the figures, identical structures, elements or parts that appear inmore than one figure are generally labeled with the same numeral in allthe figures in which they appear. Dimensions of components and featuresshown in the figures are chosen for convenience and clarity ofpresentation and are not necessarily shown to scale. The figures arelisted below.

FIG. 1 schematically shows an optical processor generating a Fouriertransform of an image according to prior art;

FIG. 2 schematically shows the optical processor shown in FIG. 1generating a cosine transform of an image in accordance with prior art;

FIGS. 3A and 3B schematically show an optical processor generating acosine transform of an image in accordance with an embodiment of thepresent invention;

FIG. 4A schematically shows an optical processor that generates areference image that is a delta function, in accordance with anembodiment of the present invention;

FIG. 4B schematically shows a lens system for generating a deltafunction reference image, in accordance with an embodiment of thepresent invention; and

FIGS. 5A-5D schematically illustrate a method of generating a cosinetransform of an image, in accordance with an embodiment of the presentinvention.

DETAILED DESCRIPTION OF EMBODIMENTS

In the following discussion an embodiment of the present invention isdescribed in which a real linear transform performed by an opticalprocessor is a cosine transform. The optical processor uses the Fouriertransform properties of converging lenses whereby a converging lenstransforms an image into its Fourier transform, to generate a cosinetransform of an image. The Fourier transform properties of lenses aredescribed in “Introduction to Fourier Optics” by J. W. Goodman, McGrawHill-Hill Companies, second edition Copyright 1996.

FIG. 1 schematically shows an optical processor 20 that functions totransform images into their Fourier transforms according to prior art.Optical processor 20 comprises a converging lens 22, an input plane 24and an output plane 26. Input and output planes 24 and 26 are coincidentwith focal planes of lens 22. It is well known that lens 22 can be usedto generate an image on output plane 26 that is a Fourier transform ofan image on input plane 24.

For example, assume that a spatial light modulator 30 having pixels 32is located at input plane 24 and that the spatial light modulator isilluminated with collimated coherent light, represented by wavy arrows34, from a suitable light source. Pixels 32 have transmittances as afunction of position that are proportional to a desired function.Spatial light modulator 30 may, for example, be a photographictransparency, a printed half tone image, a liquid crystal array or amultiple quantum well (MQW) modulator. In FIG. 1, by way of example, thetransmittances are determined so that when spatial light modulator 30 isilluminated by light 34 a happy face 36 is formed at input plane 24.Lens 22 will form an image (not shown) on output plane 26 that is theFourier transform of the happy face 36 on input plane 24.

Given a function f(x,y), the Fourier transform of the function(1/4)[f(x,y)+f(−x,y)+f(x,−y)+f(−x,−y)] is the cosine transform off(x,y). Each ofthe functions in the square brackets is a paritytransform, or a one dimensional reflection in the x or y axis, of theother functions in the brackets. It is therefore seen that the cosinetransform of a two dimensional function can be generated by Fouriertransforming all possible parity transforms of the function.

FIG. 2 illustrates how optical processor 20 shown in FIG. 1 can be usedto generate a cosine transform of an image 40 in accordance with priorart by Fourier transforming all of the image's parity transforms. Image40 may, by way of example, be an 8 by 8 block of pixels from an imagethat is to be compressed according to the JPEG standard using a discretecosine transform.

Let positions on input plane 24 and spatial light modulator 32 bedefined by coordinates along x and y axes indicated on the spatial lightmodulator and positions on output plane 26 by coordinates along u and vaxes indicated on the output plane. Let respective origins 25 and 27 ofthe x, y coordinates and the u, v coordinates be the intersections ofthe optic axis (not shown) of lens 22 with input and output planes 24and 26 respectively.

Image 40 is formed on the upper right quadrant of spatial lightmodulator 32 and reflections 42 and 44 of image 40 in the x and y axesare respectively formed in the lower right and upper left quadrants ofthe spatial light modulator. A reflection 46 of image 40 along a 45°diagonal (not shown) to the x axis through the origin is formed in thelower left quadrant of spatial light modulator 30. Let the amplitude oflight in image 40 be represented by f(x,y). Let the amplitude of lightin the image formed on input plane 24 comprising image 40 and its parityreflections be f′(x,y). Thenf′(x,y)=(1/4)[f(x,y)+f(−x,y)+f(x,−y)+f(−x,−y)]. (The decrease inamplitude by 75%, i.e. the factor 1/4, which is not necessary, can ofcourse be achieved by proper control of spatial light modulator 30). Ifthe amplitude of light in an image formed on output plane 26 by lens 22responsive to f′(x,y) is represented by F(u,v) then F(u,v) is theFourier transform of f′(x,y). Because of the symmetry of the image oninput plane 24, F(u,v) is also the cosine transform of f(x,y). If F.T.represents the operation of the Fourier transform and C.T. representsthe operation of the cosine transform then the relationships betweenF(u,v), f′(x,y) and f(x,y) is expressed by the equationF(u,v)=F.T.{f′(x,y)}=C.T.{f(x,y)}.

It is to be noted that f(x,y) and f′(x,y) represent data that is eitherall positive or all negative. For clarity of presentation datarepresented by f(x,y) is assumed to be positive. Further, since thecosine transform performed by optical processor 20 is a real lineartransform, as noted above, F(u,v) also represents real data. However,F(u,v) may have both positive and negative data. Therefore, the cosinetransform of image f(x,y) cannot be determined from the image on outputplane 26 by measuring only the intensity |F(u,v)|².

FIGS. 3A and 3B schematically show an optical processor 50 being used todetermine the sign and magnitude of the cosine transform F(u,v) of image40, i.e. f(x,y), in accordance with an embodiment of the presentinvention.

Optical processor 50 is similar to optical processor 20 and comprises alens 22, input and output planes 24 and 26. At output plane 26,processor 50 preferably comprises an array 52 of rows and columns ofphotosensors 54. Each photosensor 54 generates a signal responsive to anintensity of light in an image on output plane 26 at a positiondetermined by the row and column of array 52 in which the photosensor 54is located and a pitch of array 52. Photosensors 52 sample intensity oflight at “discrete” positions (u,v) in output plane 26. Preferably, thenumber of photosensors 52 is equal to the number of pixels 32 in spatiallight modulator 30 and the locations of photosensors 52 are homologouswith the locations of pixels 32.

In FIG. 3A, in accordance with an embodiment of the present invention,spatial light modulator 30 generates a first image at input plane 24comprising image 40 and its parity reflections 42, 44 and 46. The imageis the same as the image comprising image 40 and its reflections shownin FIG. 2. Lens 22 forms an image at output plane 26 having amplitudeF(u,v). Photosensors 54 generate signals responsive to intensity IF(u,v)of light in the image, where IF=|F(u,v)|², at their respective locationsu,v.

In FIG. 3B, in accordance with an embodiment of the present invention,spatial light modulator 30 generates a second “combined” image at inputplane 24 that comprises the image shown on the input plane in FIG. 3Awith the addition of a reference image 60 having a known amplituder(x,y). Preferably r(x,y) is chosen so that its Fourier transform isreal, i.e. it has a symmetry with respect to the origin of axes x and ywhich results in its Fourier transform being real. By way of example, inFIG. 3B, reference image 60 is formed by controlling central pixels 61,62, 63 and 64 located at the origin of coordinates of input plane 24 totransmit light and appear bright.

If c(x,y)=(f′(x,y)+r(x,y)) then lens 22 forms an image (not shown) onoutput plane 26 that is the Fourier transform of c(x,y) and photosensors54 generate signals responsive to intensity, IC(u,v), of light in theimage. If C(u,v) represents the Fourier transform of c(x,y), then theamplitude of light in the image is C(u,v)and IC(u,v)=|C(u,v)|².

In accordance with some embodiments of the present invention IF(u,v),IC(u,v) and the known Fourier transform of r(x,y) are used to determinethe magnitude and sign of F(u,v) and thereby the cosine transform off(x,y).

C(u,v)=F.T.{c(x,y)}=F.T.{f′(x,y)+r(x,y)}=F.T.{f′(x,y)}+F.T.{r(x,y)}=F(u,v)+R(u,v),where R(u,v) is the known and/or measured Fourier transform of r(x,y).Therefore,IC(u,v)=[|F(u,v)|²+|R(u,v)|²+2F(u,v)R(u,v)]=IF(u,v)+IR(u,v)+2F(u,v)R(u,v),where IR(u,v)=|R(u,v)|². IR(u,v) can be calculated from the knownFourier transform of r(x,y) or measured experimentally. In someembodiments of the present invention the sign and magnitude of F(u,v)are determined from the equationF(u,v)=[IC(u,v)−IF(u,v)−IR(u,v)]/2R(u,v).

In some embodiments of the present invention the magnitude of F(u,v) isdetermined from the square root of IF(u,v). The sign of F(u,v) can bedetermined by comparing IF(u,v) and IR(u,v) with IC(u,v). IfIF(u,v) >IC(u,v) or IR(u,v) >IC(u,v) then R(u,v) and F(u,v) haveopposite sign. Otherwise they have the same sign. Since the sign ofR(u,v) is known the sign of F(u,v) is known.

Whereas, in FIGS. 3A and 3B reference image 60 is a symmetric imagelocated at the center of origin of the x,y coordinates other referenceimages are possible and can be used in the practice of the presentinvention. For example, pixels 32 at the corners of spatial lightmodulator 30 can be used to generate useful reference images. In someembodiments of the present invention pixels 32 only in certain regionsof spatial light modulator 30 are used to represent data. Pixels thatare not needed for data are used, in some embodiments of the presentinvention, to generate reference images. In some embodiments, some datapixels are canceled or provided elsewhere n the image, for example aspixels in overlapping blocks. In other examples extra pixels areprovided for the reference image, for example by inserting one or morerows or columns per block. For example “data” pixels may be restrictedto alternate rows or columns of pixels. Or each data pixel may besurrounded by four pixels that are not used for data. In an exemplaryembodiment, 9×9 blocks of data are used for an 8×8 block transform, withat least some ofthe extra pixels being used as a reference image.alternatively or additionally, the effect of missing pixels may becorrected using an electronic or optical post processing step.

It should also be noted that dark pixels, pixels that are “turned off”,that do not transmit light can function to generate reference images.For example, if an image on spatial light modulator 30 has bright pixelsat the origin of coordinates (i.e. pixels 61, 62, 63 and 64 in FIG. 3B)a reference image can be generated by “turning off” the pixels. Turningoff pixels in an image is of course equivalent to adding a referenceimage to the image for which light at the turned off pixels has a phaseopposite to that of the light in the image.

In some embodiments of the present invention, reference image f(x,y) ischosen so that |R(u,v)|≧|F(u,v)| for all values of u and v for whichR(u,v) and F(u,v) have opposite signs. For these embodiments of thepresent invention it is not necessary to determine IF(u,v) and only theoperation shown in FIG. 3B in which IC(u,v) is measured is required todetermine the magnitude and phase of F(u,v). If at a point (u,v),IC(u,v)−IR(u,v) >0 then the signs F(u,v) and R(u,v) are the same at thepoint otherwise the signs are opposite. The magnitude of F(u,v) at thepoint can be determined from IC(u,v) by solving the quadratic equationIC(u,v)=[|F(u,v)|²+|R(u,v)|²+2F(u,v)R(u,v)] for F(u,v).

FIG. 4A schematically shows a side view of an optical processor 70, inaccordance with an embodiment of the present invention, that generates areference field for which |R(u,v)|>|F(u,v)| for all values of u and vfor which R(u,v) and F(u,v) have opposite signs.

Optical processor 70 comprises a “Fourier” lens 22 having an outputplane 26 coincident with a focal plane of lens 22, a spatial lightmodulator 72 and a “beam partitioner” 74. A detector array 76 is locatedat output plane 26 and measures intensity of light at the output plane.Spatial light modulator 72 defines an input plane for Fourier lens 22and may be located at substantially any position to the left of outputplane 26. In optical processor 70 spatial light modulator 72 is locatedby way of example adjacent to lens 22.

Beam partitioner 72 preferably receives an incident beam 78 of coherentcollimated light generated by an appropriate source (not shown) andfocuses a portion of the light to a point 80 and transmits a portion ofthe light as a transmitted beam of light 82 parallel to the incidentbeam. Light from transmitted beam 82 illuminates and is transmittedthrough spatial light modulator 72 and is focused by lens 22 to form aFourier transform F(u,v) of a transmittance pattern f(x,y) formed on thespatial light modulator. It is assumed that the transmittance patternhas an appropriate symmetry so that the Fourier transform is a cosinetransform of a desired image.

Point 80 functions substantially as a point source of light and providesa reference image r(x,y) for f(x,y) that is substantially a deltafunction Aδ(x,y), where A is proportional to an intensity of lightfocused to point 80. A Fourier image, R(u,v), of light from point 80 isalso formed on output plane 26 by lens 22. Since r(x,y) is substantiallya delta function, R(u,v) is substantially constant and equal to A.

The magnitude of F(u,v) at a point (u,v) is of course proportional tothe intensity of light in transmitted beam 82. In accordance with anembodiment of the present invention beam partitioner 74 is designed sothat the relative portions of light focused to point 80 and transmittedin transmitted beam 82 beam are such that A=|R(u,v| is greater than|F(u,v)| for all values of u and v for which R(u,v) and F(u,v) haveopposite signs.

In some embodiments of the present invention beam partitioner 74 is adiffractive optical element such as a Fresnel zone plate having reducedefficiency. In some embodiments of the present invention, beampartitioner 74 comprises an optical system 90 of a type shown in a sideview in FIG. 4B. Optical system 90 comprises a positive lens 92 and aweak negative lens 94. Positive lens 92 is preferably coated with anantireflective coating using methods known in the art to minimizereflections. Weak negative lens 92 is treated so that at its surfaceslight is reflected with a reflectivity α. Light from incident beam 78,represented by arrowed lines 96, that is transmitted through bothpositive lens 92 and negative lens 94 without reflections is focused toproduce the point reference light source Aδ(x,y) at point 80. If theintensity of light in light beam 78 is “I” the amount of light focusedto point 80 is substantially equal to I(1−α)². Light that undergoesinternal reflection twice in negative lens 94 is transmitted astransmitted beam of light 82 substantially parallel to incident beam 78.The amount of energy in transmitted beam 82 is substantially equal toI(1−α)²α². The ratio of energy focused to point 80 to that contained intransmitted beam && is therefore equal to 1/α².

In accordance with an embodiment of the present invention R can bechosen so that A=|R(u,v| is greater than |F(u,v)| for all values of uand v for which R(u,v) and F(u,v) have opposite signs.

Given a function f(x,y) it can be shown that the cosine transformC.T.f(x,y)=1/2[ReF.T.{f(x,y)}+ReF.T.{f(x,−y)}]=1/2[ReF_(p)(u,v)+ReF_(m)(u,v)]where Re indicates the real part of a complex number and F_(p)(u,v) andF_(m)(u,v) are the Fourier transforms of f(x,y) and f(x,−y)respectively.

Let c_(p)(x,y)=f(x,y)+A_(p)δ(x,y) and c_(m)(x,y)=f(x,−y)+A_(m)δ(x,y).The Fourier transform, C_(p)(u,v), of c_(p)(x,y) may be writtenC_(p)(u,v)=[F_(p)(u,v)+A]=[ReF_(p)(u,v)+Im F_(p)(u,v)+A_(p)], where Imindicates the imaginary part of a complex number and A_(p) is assumed tobe real. Similarly the Fourier transform of c_(m)(x,y) may be writtenC_(m)(u,v)=[F_(m)(u,v)+A_(m)]=[ReF_(m)(u,v)+Im F_(m)(u,v)+A_(m)].

If the “intensities” of the Fourier transforms F_(p)(u,v) and C_(p)(u,v)are written as IF_(p)(u,v) and IC_(p)(u,v) respectively so thatIF_(p)(u,v)=|F_(p)(u,v)|² and IC_(p)(u,v)=|C_(p)(u,v)|² then it can beshown that ReF_(p)(u,v)=[IC_(p)(u,v)−IF_(p)(u,v)−A_(p) ²]/2A_(p).Similarly, ReF_(m)(u,v)=[IC_(m)(u,v)−IF_(m)(u,v)−A_(m) ²]/2A_(m) whereIF_(m)(u,v)=|F_(m)(u,v)|² and IC_(m)(u,v)=|C_(m)(u,v)|².

Therefore the cosine transform of f(x,y) can be determined from theintensities IF_(p)(u,v), IC_(p)(u,v) and A_(p) and IF_(m)(u,v),IC_(m)(u,v) and A_(m). It should be noted that whereas a delta functionhas been added as a reference field for f(x,y) and f(x,−y) in the abovecalculations, similar results can obtain for other reference functionsr(x,y). FIGS. 5A-5D illustrate a method, in accordance with anembodiment of the present invention by which the functions IF_(p)(u,v),IC_(p)(u,v) and A_(p) and IF_(m)(u,v), IC_(m)(u,v) and A_(m) areevaluated using an optical processor 100 to generate a cosine transformof a function f(x,y). Optical processor 100 is similar to opticalprocessors 50 and 70 and comprises a Fourier lens 22, a photosensorarray 52 at an output plane 26, which is located at a focal plane oflens 22 and a spatial light modulator 30.

Referring to FIG. 5A assume that function f(x,y) is represented by animage 40 formed by spatial light modulator 30. Optical modulator 100generates the Fourier transform F(u,v) of f(x,y) and acquires values forIF_(p)(u,v). In FIG. 5B, a point light source 102 generates a deltafunction reference A_(p)δ(x,y) image which is added to f(x,y) to form animage c_(p)(x,y)=f(x,y)+A_(p)δ(x,y). Processor 100 Fourier transformsc_(p)(x,y) and acquires IC_(p)(u,v). Point light source may be providedusing any methods known in the art. In some embodiments of the presentinvention point light source is provided by methods and apparatus thatare similar to those described in the discussion of FIGS. 4A and 4B.

In FIG. 5C, spatial light modulator 30 forms an image f(x,−y) andacquires IF_(m)(u,v). In FIG. 5D a delta function reference functionA_(m)δ(x,y) is added to f(x,−y) and IC_(m)(u,v) is acquired. A suitableprocessor (not shown) receives the acquired data and uses it todetermine ReF_(p)(u,v) and ReF_(m)(u,v) from which the cosine transformof f(x,y) may be determined as shown above.

The present application is related to the following four PCTapplications, all filed on May 19, 2000: PCT/IL00/00282 published as WO00/72105, which especially describes matching of discrete and continuousoptical elements, PCT/IL00/00285 published as WO 00/72107 whichespecially describes reflective and incoherent optical processordesigns, PCT/IL00/00283 published as WO 00/72104 which especiallydescribes various architectures for non-imaging or diffractive basedoptical processing, and PCT/IL00/00286 published as WO 00/72108 whichespecially describes a method of processing by separating a data setinto bit-planes and/or using feedback. The disclosures of all of theseapplications are incorporated herein by reference.

In the description and claims of the present application, each of theverbs, “comprise” “include” and “have”, and conjugates thereof, are usedto indicate that the object or objects of the verb are not necessarily acomplete listing of members, components, elements or parts of thesubject or subjects of the verb.

The present invention has been described using detailed descriptions ofembodiments thereof that are provided by way of example and are notintended to limit the scope of the invention. The described embodimentscomprise different features, not all of which are required in allembodiments of the invention. Some embodiments of the present inventionutilize only some of the features or possible combinations of thefeatures. Variations of embodiments of the present invention that aredescribed and embodiments of the present invention comprising differentcombinations of features noted in the described embodiments will occurto persons of the art. The scope of the invention is limited only by thefollowing claims.

1. A method of optical data processing, comprising: providing a first data set to be optically transformed using a transform; combining a reference data set with said first data set to generate coherent light, encoding a combined data set; optically and coherently transforming said light that encodes the combined data set, into coherent light that encodes a transformed combined data set; obtaining a transformed reference data set by determining the effect said optical transform has on light encoding said reference data set; and extracting a second data set that represents a transform of said first data set, from an intensity portion of light encoding said transformed combined data set, using said transformed reference data set to extract a phase of at least one element of said second data set.
 2. A method according to claim 1, wherein said transformed combined data set is detected using a power detector.
 3. A method according to claim 1, wherein said transformed combined data set is encoded using incoherent light, after said coherent transforming.
 4. A method according to claim 1, wherein said transformed combined data set is a discrete data set.
 5. A method according to claim 1, wherein said first data set comprises a one-dimensional data set.
 6. A method according to claim 1, wherein said first data set comprises a two-dimensional data set.
 7. A method according to claim 6, wherein said first data set comprises an image.
 8. A method according to claim 1, wherein said first data set comprises at least one positive value.
 9. A method according to claim 1, wherein said first data set comprises at least one negative value.
 10. A method according to claim 1, wherein said first data set comprises at least one complex value.
 11. A method according to claim 1, wherein extracting comprises extracting using electronic processing.
 12. A method according to claim 1, wherein combining a reference data set comprises adding at least one additional value to an existing element of said first data set.
 13. A method according to claim 1, wherein combining a reference data set comprises replacing at least one existing element of said first data set with an element from a second data set.
 14. A method according to claim 13, comprising compensating for an effect of said replaced value after said extraction.
 15. A method according to claim 14, wherein said compensating comprises compensating using electronic processing.
 16. A method according to claim 1, wherein combining a reference data set comprises adding at least one additional value alongside existing elements of said first data set.
 17. A method according to claim 16, wherein said at least one additional value is arranged at a corner of a matrix layout of said first data set.
 18. A method according to claim 1, comprising selecting said reference image to create a desired offset in said transformed combined data set.
 19. A method according to claim 18, wherein said selecting takes into account system imperfections.
 20. A method according to claim 18, wherein said offset is substantially uniform. 